Climate Change: Day 10

date: September 25, 2014

Last Time: jet stream, arctic amplification, extra-tropical cyclones, more hot days in Tally

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L = "http://myweb.fsu.edu/jelsner/PW_US.txt"
df = read.table(L, header = TRUE)
head(df)
##   Month Year  AvgPW MoA     PW
## 1     1 1958 0.2968 Jan 0.7538
## 2     1 1959 0.3324 Jan 0.8443
## 3     1 1960 0.3399 Jan 0.8634
## 4     1 1961 0.2716 Jan 0.6900
## 5     1 1962 0.3124 Jan 0.7934
## 6     1 1963 0.2688 Jan 0.6828
library(ggplot2)
ggplot(df, aes(x = Year, y = PW)) +
  geom_line() +
  geom_smooth(method = lm) +
  facet_wrap(~ Month, nrow = 1) +
  ylab("US Avg Monthly Precipitable Water (cm)") +
  theme_bw()

plot of chunk unnamed-chunk-1

  • Slower moving jet stream together with more moisture (water vapor) increases the chance for heavy rainfall.

  • The atmosphere’s ability to hold water (recall: saturation vapor pressure vs temp) increases by about 4 percent for every 1°F increase in temperature

  • Heavy precipitation fact sheet WRI

  • 1-in-100 year event. Return periods versus annual probability.

Today: tropical cyclones, heat engine, MPI vs LI

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\[ \hbox{MPI} \sim \frac{\hbox{SST}}{T_o}\hbox{BL}_{f}(\hbox{SST}) \]

MPI (maximum potential intensity) is the highest wind speed (rotational) in units of meters per second.

SST is the ocean temperature at the surface, \(T_o\) is the temperature at the top of the hurricane and BL\(_{f}\)(SST) is the heat flux near the ocean surface. The heat flux depends on SST.

Extreme value theory (EVT) is a statistical theory that estimates the risk of extreme, rare events.

Suppose we record the highest wind speed (m s\(^{-1}\)) from 10 consecutive hurricanes.

  • 34.5, 44.2, 57.5, 33.8, 67.8, 38.2, 41.5, 71.2, 61.0, 49.1

We order the values from lowest to highest.

  • 33.8, 34.5, 38.2, 41.5, 44.2, 49.1, 57.5, 61.0, 67.8, 71.2

This tells us that 20% of the hurricanes have winds that exceed 61 m s\(^{-1}\) and 10% have winds that exceed 67.8 m s\(^{-1}\). EVT uses these quantile wind speeds to work out a theoretical highest possible wind speed, which we will call the limiting intensity (LI).

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